Solve the problem by working backwards and explaining each step Pennies in the S

Question

Solve the problem by working backwards and explaining each step

Pennies in the Sand!

I hate taking my little brother, Cal, to the park. All he does is find ways to cause trouble. For example, the other day he took a bunch of pennies to the park. He promptly lost 2?5 of them and cried. I stopped swinging and helped him look for them. He managed to let three more fall out of his pocket while we were looking. When I tried to grab them before they sank in the sand, he threw a temper tantrum and lost another 1?3 of the pennies he had left. I gave him ten pennies from my pocket to try to stop him from crying, but that didn’t help. He then got mad and started throwing them. He threw away 3?4 of his remaining pennies and ended up with seven. We looked for them some more but found a lot of cigarette butts and no pennies. How much money did my brother lose at the park? I don’t know, but I would have gladly paid him that much not to go to the park. Find out how much Cal lost at the park.

Explanation / Answer

Let the number of pennies with brother be x

After loosing 2/5th of pennies = x - 2/5x = 3/5x

Lost three more pennies, pennies left = 3/5x - 3

Lost another 1/3rd of pennies, so pennies left = (3/5x - 3) - 1/3 * (3/5x -3) = 3/5x - 3 - 1/5x + 1 = 2/5x - 2

Gave 10 pennies from my pocket, so pennies became 2/5x - 2 + 10 = 2/5x + 8

Thrown 3/4th of the remaining pennies, pennies left = 2/5x + 8 - 3/4 * (2/5x + 8) = 2/5x + 8 - 6 - 3/10x = x/10 + 2

The final pennies count is equal to 7

Hence we get

x/10 + 2 = 7

x/10 = 5, x = 50

Hence the brother bought 50 pennies with him to the park

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